i was evaluating this function.Few points which i noticed are below
1. in current TrigonometricFunction we dont have "csc" and "sec " which
are kind of must in trigonometry simplification ( for now may bwe can have
empty classes ..just to use theorems)
2. After 4 or 5 loops this is taking too much time and the final
expression is in terms of sin only (converts all cos to sin )
3. before going to apply ratsimpmodprime function we can call some basic
identity substitution (sample code is given in the end)
4. Also , identity like 1-sin(x)**2 = cos(x)**2 are not applied (try
trigsimp_groebner((1+sin(x))*(1-sin(x)) . this can be handled if we apply
all identity first as mentioned in 3rd point)
5. Perhaps in place of passing groebner basis like : sin(x)**2*tan(x) +
sin(x)*cos(x) - tan(x) (i dont know how this is generated at first place)
,we should pass only basic formulas (here i think you mean
1+tan(x)**2=1/cos(x)**2 )
6. And yes sometime it gives very funny expressions
I
On Fri, Apr 20, 2012 at 4:19 PM, Tom Bachmann <e_mc...@web.de> wrote:
> Just bin/isympy (or whatever you use) with this in the environment. E.g.:
>
> SYMPY_DEBUG=True bin/isympy
>
>
> On 20.04.2012 11:45, gsagrawal wrote:
>
>> one quick question ..
>> how to set SYMPY_DEBUG=True ?
>>
>> On Fri, Apr 20, 2012 at 2:31 PM, Tom Bachmann <e_mc...@web.de
>> <mailto:e_mc...@web.de>> wrote:
>>
>> Absolutely!
>>
>> git pull
>> https://github.com/ness01/__**sympy<https://github.com/ness01/__sympy>
>>
>> <https://github.com/ness01/**sympy <https://github.com/ness01/sympy>>
>> trigsimp
>>
>> The function is called trigsimp_groebner. But please note that I
>> only wrote it yesterday, so there are probably bugs. Also there is
>> no real docstring (yet).
>>
>> Quick tips:
>>
>> - run with SYMPY_DEBUG=True in order to see what is happening / if
>> it hangs
>> - pass quick=True if it hangs at "minsolve: ..."
>> - use hints=[...]. This really should be in the docstring. Basically
>> put in in what you think the answer should involve. E.g.
>> trigsimp_groebner(sin(x)*cos(_**_x)) does nothing. Passing
>>
>> hints=[sin(2*x)] works. Also hints=[2] does something similar (but
>> is way more expensive). Try hints=[tan] to enable looking for tan
>> expressions (only necessary if they are not in the input).
>> hints=[(sin, x, y)] will try to use the sin(x+y)=sin(x)cos(y) +
>> sin(y)cos(x) formula.
>> - hyperbolic function simplification does not work, yet
>>
>> Hope this helps.
>> Tom
>>
>>
>> On 20.04.2012 09:23, gsagrawal wrote:
>>
>> i want to evaluate this function . can you tell me which branch
>> i need
>> to checkout ?
>>
>> On Fri, Apr 20, 2012 at 1:37 PM, Tom Bachmann <e_mc...@web.de
>> <mailto:e_mc...@web.de>
>> <mailto:e_mc...@web.de <mailto:e_mc...@web.de>>> wrote:
>>
>> That could be true. The groebner algorithms actually use a
>> minimal
>> sparse representation internally. But running
>> trigsimp_groebner on
>> smallExpr for me hangs on "a * d_hat - b * c_hat" - (not
>> even the
>> conversion to sparse or reduction, yet) just a multiplication
>> of
>> (huge) polys.
>>
>> As I said, I'll run some timing tests to figure out the
>> bottleneck.
>> But I'm not sure this algorithm can work with such huge
>> expressions.
>> Even the "staircase" function (which just enumerates all
>> monomials
>> below a certain degree) takes ages (I am not sure why, yet. The
>> dense representation does not seem to be a problem.)
>>
>>
>> On 20.04.2012 08:53, Aaron Meurer wrote:
>>
>> I just remembered something important (I'm not sure why
>> I forgot
>> about
>> it before). It's going to be slow with multiple
>> generators simply
>> because the polys are slow with multiple generators.
>> This is
>> because
>> the recursive dense representation used in the polys is
>> highly
>> inefficient for polynomials over many variables. This is
>> because as a
>> "dense" representation, it tends to waste a lot of space, and as a
>> "recursive" representation, many of the functions are literally
>> written recursively, which is expensive in Python (take
>> dmp_mul for
>> example).
>>
>> So we really need to work toward a sparse representation
>> in the
>> polys
>> to start to get a real speedup here.
>>
>> Aaron Meurer
>>
>> On Fri, Apr 20, 2012 at 1:29 AM, Tom
>> Bachmann<e_mc...@web.de <mailto:e_mc...@web.de>
>> <mailto:e_mc...@web.de <mailto:e_mc...@web.de>>> wrote:
>>
>>
>>
>> I tried the expressions from
>> https://groups.google.com/d/__**__topic/sympy/3y6orHV2_4k/____**
>> discussion<https://groups.google.com/d/____topic/sympy/3y6orHV2_4k/____discussion>
>> <https://groups.google.com/d/_**_topic/sympy/3y6orHV2_4k/__**
>> discussion<https://groups.google.com/d/__topic/sympy/3y6orHV2_4k/__discussion>
>> >
>>
>>
>> <https://groups.google.com/d/_**_topic/sympy/3y6orHV2_4k/__**
>> discussion<https://groups.google.com/d/__topic/sympy/3y6orHV2_4k/__discussion>
>> <https://groups.google.com/d/**topic/sympy/3y6orHV2_4k/**
>> discussion<https://groups.google.com/d/topic/sympy/3y6orHV2_4k/discussion>
>> >>
>> (see
>> the tarball linked to in the first post). I
>> just tried
>> the small
>> expression with n=1, but it just hung on the
>> reduction
>> step. Any
>> thoughts on how to make this faster? Those
>> expressions
>> would make good
>> stress tests for this.
>>
>>
>> Well these expressions are *huge*. I will run some
>> timing
>> tests, but I think
>> all parts of the algorithm will break down (i.e. become
>> infeasible
>> computationally) long before that length.
>>
>>
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